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Fight-the-Streets said:

According to the most updated data we have available, the PS2 sold a minium of 158.6mil. and a maximum of 161mil. (and it is generally agreed that the number most probably is at the lower end of the spectrum). So in no way it is possible that the PS2 sold more than 161mil. Once the Switch reaches 155mil. I'm pretty sure it coughs itself past the 161mil. (unless it already had to cough itself to 155mil.)

Actually, I have to correct myself, the mathematical absolute minimum the PS2 sold is 159.2mil. and the mathematical absolute maximum is 161.9mil, taken from Resetera: https://www.resetera.com/threads/what-was-the-lifetime-sales-of-the-ps2-not-158m-update-between-159-2m-and-161-9m.77277/

Two snippets out of the discussion from ZhugeEX (Senior Analyst at Niko Partners):

1.
It's fairly simple.

PS2 Production Shipments were 117.9 million as of March 2007.
At this point Sony switched from reporting production shipments to hardware sell in.
Hardware sell in at this point was 115.6 million. So you can see there is a slight difference between Production Shipments vs Hardware sell in due to difference in reporting methods.

PS2 sold a further 39.5 million units through to March 2012 which takes the sell in total to 155.1 million.

In the fiscal year ending March 2013 a total of 16.5 million PS3&PS2 units were shipped. PS2 was still being shipped during this period so the info we're missing is how many units were PS2 and how many were PS3. Using PS3's 80m sell in announcements as a guide you can work backwards and ultimately work out that PS2 must have been close to 4m.

So whilst we don't know the 'official' number. We do know it was 155.1m as of March 2012 and there was another few million shipped shipped during the 9 months after that.

2.
The minimum would be 4.1m in FY12 and the maximum would be 6.8m.

PS2 is likely up YoY in FY12 as it is not mentioned as being down, like it is in prior reports. So with that in mind, and to align with PS3 hitting 80m in November we can say PS2 LTD is a minimum of 159.2m and a maximum of 161.9m. Most likely being closer to the former number.

I think the number must be closer to 159.2mil because 1. the PS2 was on it's very last leg in FY2013, so it's only logical that the shipping numbers must have been at the lower end and 2. if the PS2 would have sold 160mil, certainly, Sony would have reported it as it makes sense to report such a milestone, like it has announced the 150mil mark.

For me personally, if the Switch reaches 160mil, it will have definitely sold out the PS2 unless Sony or some credible source (like Shawn Layden came up with the exact lifetime sales of the PSP) come up with a definitive number. However, I hope the Switch will reach 162mil as at that point it's mathematically proven that it sold out the PS2. I hope that not as a Nintendo-Fanboy but because it would put an end to all theoretical discussions.